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arXiv · 0906.1261

On moduli of rings and quadrilaterals: algorithms and experiments

Harri Hakula·Antti Rasila·Matti Vuorinen
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Abstract

Moduli of rings and quadrilaterals are frequently applied in geometric function theory, see e.g. the Handbook by K\"uhnau. Yet their exact values are known only in a few special cases. Previously, the class of planar domains with polygonal boundary has been studied by many authors from the point of view of numerical computation. We present here a new $hp$-FEM algorithm for the computation of moduli of rings and quadrilaterals and compare its accuracy and performance with previously known methods such as the Schwarz-Christoffel Toolbox of Driscoll and Trefethen. We also demonstrate that the $hp$-FEM algorithm applies to the case of non-polygonal boundary and report results with concrete error bounds.

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Harri Hakula, Antti Rasila, Matti Vuorinen. 2009-06-06. On moduli of rings and quadrilaterals: algorithms and experiments. https://doi.org/10.1137/090763603

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